Question: Solve for $x$ : $7\sqrt{x} - 10 = 2\sqrt{x} + 7$
Solution: Subtract $2\sqrt{x}$ from both sides: $(7\sqrt{x} - 10) - 2\sqrt{x} = (2\sqrt{x} + 7) - 2\sqrt{x}$ $5\sqrt{x} - 10 = 7$ Add $10$ to both sides: $(5\sqrt{x} - 10) + 10 = 7 + 10$ $5\sqrt{x} = 17$ Divide both sides by $5$ $\frac{5\sqrt{x}}{5} = \frac{17}{5}$ Simplify. $\sqrt{x} = \dfrac{17}{5}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{17}{5} \cdot \dfrac{17}{5}$ $x = \dfrac{289}{25}$